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On discovery and exploitation of temporal structure in data sets

This is my PhD thesis supervised by Dr Yuri Kalniskan and Professor Alex Gammerman

This thesis explores temporal structure based on self-similarity in different

An efficient dynamic programming algorithm is presented which discovers temporal
structures in music shows, obtains high quality results, and compares them to
similar algorithms used in the literature.  The program segments a
self-similarity matrix given a cost function and a fixed number of homogeneous
temporal structures to find. This is the initial approach we use to discover
temporal structures in music data.

The use of a self-similarity matrix to visualize temporal structures is
discussed in detail. Then the following question is explored; if similar
temporal structures in other corpora existed; could forecasting algorithms be
adapted to take advantage of them even if they were not known a priori?

Prediction with expert advice techniques are then introduced to exploit a priori
unknown temporal structures of a similar configuration in an on-line
configuration. Uni-variate Russian Stock Exchange options futures volatility
corpora are used, which are highly interesting for on-line forecasting.

We experiment with merging together expert models which have been trained in
some way to recognise temporal structures in corpora. The first types are kernel
ridge regression models trained to be experts on particular regions in time, or
untrained and given random sets of parameters which may work well on certain
time regions. The other types of model used are parsimonious predictors which
transform uni-variate financial data into elementary time series based on
homogeneous vicinities of information in the side domain. Expert merging
techniques are then used across these time series which produce a
validation-free forecaster comparable to sliding kernel ridge regression.